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Section 3: Design Frequency

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Concept of Frequency

As with other natural phenomena, occurrence of flooding is governed by chance. The chance of flooding is described by a statistical analysis of flooding history in the subject watershed or in similar watersheds. Because it is not economically feasible to design a structure for the maximum possible runoff from a watershed, the designer must choose a design frequency appropriate for the structure.

The expected frequency for a given flood is the reciprocal of the probability or chance that the flood will be equaled or exceeded in a given year. For example, if a flood has a 20 percent chance of being equaled or exceeded each year, over a long period of time the flood will be equaled or exceeded on an average of once every five years. This is called the return period or recurrence interval (RI). Thus the exceedance probability equals 100/RI. The following table lists the probability of occurrence for the standard design frequencies.

Anchor: #i1010271Frequency versus Probability

Frequency (Years)

Probability (%)

2

50

5

20

10

10

25

4

50

2

100

1


The five-year flood is not one that will necessarily be equaled or exceeded every five years. There is a 20 percent chance that the flood will be equaled or exceeded in any year; therefore, the five-year flood could conceivably occur in several consecutive years. The same reasoning applies to floods with other return periods.

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Frequency Determination

Derive the design frequency from the importance of the appropriate highway, the level of service, potential hazard to adjacent property, future development, and budgetary constraints. Develop alternative solutions that satisfy design considerations to varying degrees. After evaluating each alternative, select the design that best satisfies the requirements of the structure. Additional considerations include the design frequencies of other structures along the same highway corridor to ensure that the new structure is compatible with the rest of the roadway and the probability of any part of a link of roadway being cut off due to flooding. Address the list of considerations using either design by frequency selection or by examples for cost optimization or risk assessment.

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Design by Frequency Selection

A traditional approach to establishing a frequency for design of a drainage facility is by use of reference tables in which specific ranges of design frequencies are established for different facility types. The following table presents recommended ranges for possible use on TxDOT projects. Inundation of the travelway dictates the level of traffic service provided by the facility. The travelway overtopping flood level identifies the limit of serviceability. This table relates desired minimum levels of protection from travelway inundation to functional classifications of roadways. For the selected design frequency, design the facility to avoid inundation of the roadway.

Anchor: #i1010296Recommended Design Frequencies (years)

 

Design

Check Flood

Functional Classification and Structure Type

2

5

10

25

50

100

Freeways (main lanes):

 

 

 

 

 

 
  • culverts

 

 

 

 

X

X
  • bridges

 

 

 

 

X

X

Principal arterials:

 

 

 

 

 

 
  • culverts

 

 

X

(X)

X

X
  • small bridges

 

 

X

(X)

X

X
  • major river crossings

 

 

 

 

(X)

X

Minor arterials and collectors (including frontage roads):

 

 

 

 

 

 
  • culverts

 

X

(X)

X

 

X
  • small bridges

 

 

X

(X)

X

X
  • major river crossings

 

 

 

X

(X)

X

Local roads and streets (off-system projects):

 

 

 

 

 

 
  • culverts

X

X

X

 

 

X
  • small bridges

X

X

X

 

 

X

Storm drain systems on interstate and controlled access highways (main lanes):

 

 

 

 

 

 
  • inlets and drain pipe

 

 

X

 

 

X
  • inlets for depressed roadways*

 

 

 

 

X

X

Storm drain systems on other highways and frontage:

 

 

 

 

 

 
  • inlets and drain pipe

X

(X)

 

 

 

X
  • inlets for depressed roadways*

 

 

 

(X)

X

X

Notes.

* A depressed roadway provides nowhere for water to drain even when the curb height is exceeded.

( ) Parentheses indicate desirable frequency.


In establishing a design frequency for a drainage facility, the designer takes the risk that a flood may occur that is too large for the structure to accommodate. This risk is necessary when limited public funding is available for the drainage facility. Using the “Recommended Design Frequencies” table only implies but does not quantify the level of risk. For many projects, you may determine the potential risks associated with design by frequency selection to be so small that you would need no further appraisal of risk. However, if contemplating deviation from the recommended design frequencies or the potential risks could be significant, perform a risk assessment. The extent of this assessment should be consistent with the value and importance of the facility.

NOTE: Federal law requires interstate highways to be provided with protection from the 50-year flood event, and facilities such as underpasses, depressed roadways, etc., where no overflow relief is available should be designed for the 50-year event.

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Design by Cost Optimization or Risk Assessment

The objective of cost optimization is to choose a design frequency that results in a facility that satisfies all the design requirements with the lowest total cost. Structures with low design frequencies generally have lower capital costs but higher operational costs. In discussions of cost optimization, the following definitions apply:

  • Capital costs are those associated with the direct construction of a facility that can be readily estimated. Generally, the higher the design frequency, the higher the capital cost.
  • Operational costs are associated with maintenance and repair to the facility and costs of any damage incurred by the facility. For the hydraulic design of drainage structures, the primary concern is the potential for flood damage and risk to the traveling public.

A large structure with a high design frequency may have a much larger capital cost yet lower operational costs. The larger structure may last through several lifetimes of the smaller structure. In addition, potential costs of interruption to traffic and other damage may be higher for the smaller structure. Figure 5-2 shows a plot of the cost for design alternatives of varying design frequency. The optimal design is the one that balances capital costs with operational costs to produce the lowest total cost.

Lowest Total Expected Cost (click in image to see full-size image) Anchor: #i998978

Figure 5-2. Lowest Total Expected Cost

Risk is defined as the consequences associated with the probability of flooding. For low frequency designs, the probability of flood-related damage is usually higher than that associated with higher frequency designs. A risk assessment involves appraising the levels of risk for selected design alternatives and is less extensive than a cost optimization approach.

FORMC1 provides examples of forms using risk assessment in bridge design. FORMC2 shows supplemental worksheets for summarizing economic risk and losses. The FHWA publication Design of Encroachments on Flood Plains Using Risk Analysis, Hydraulic Engineering Circular Number 17 (HEC #17), provides more extensive detail on risk assessment and cost optimization. Although the forms, worksheets, and the example in HEC # 17 refer to bridge design, risk assessment should not be limited to bridges. The same approach is valid for the design of most drainage facilities.

Design by cost optimization or risk assessment can be largely subjective, and data requirements often are much more extensive than design by frequency selection. The following examples illustrate situations in which either cost optimization or risk assessment might be appropriate:

  • Replacement of off-system bridges where an existing facility has lower capacity than the recommended design frequency for given hydrologic conditions. Usually, off-system bridges are replaced for reasons other than hydraulic adequacy. A risk assessment would help to justify whether a structure larger than the existing structure is needed.
  • Where there is a need to determine whether cost of exceeding 50-year design frequency for a floodplain crossing is justifiable.
  • To justify any design that falls within the design frequencies recommended in the “Recommended Design Frequencies” table.
  • A drainage facility type is not addressed in “Recommended Design Frequencies” table.
  • Required roadway improvements where existing drainage facilities are in good condition but do not meet recommended design frequency. A risk assessment should be employed to determine if existing structures should be replaced.
  • Any situation in which the potential risks of damage are high or questionable.
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Check Flood Frequencies

Most flood events are of smaller magnitude than the design flood, but a few are of greater magnitude. From the standpoint of facility utilization, strive toward a facility that will operate in the following manner:

  • efficiently for lesser floods
  • adequately for the design flood
  • acceptably for greater floods.

For these reasons, it is often important to consider floods of other magnitudes. To define the peak flows for frequencies other than the design frequency, use the approach of developing a general flood-frequency relation for the subject site.

For all drainage facilities, including storm drain systems, evaluate the impact of the 100-year flood event. In some cases, evaluate a flood event larger than the 100-year flood (super-flood) to ensure the safety of the drainage structure and downstream development. A 500-year flood analysis is required for checking the design of bridge foundations against potential scour failure.

If a catastrophic failure of a bridge or culvert can release a flood wave that would result in loss of life, disruption of essential services, or excessive economic damage, the bridge or culvert design should be evaluated in terms of a probable maximum flood or PMF. For example, a culvert under normal flood operation will act like a dam. PMF considers the conditions under which the culvert/dam may fail. The PMF is not related to an event frequency but is a specialized analysis. Consult the Bridge Division’s Hydraulic Branch for assistance with the PMF determination.

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Frequencies of Coincidental Occurrence

Where the outfall of a system enters as a tributary of a larger drainage basin, the stage-discharge characteristics of the outfall may operate independently of the main drainage basin. This is especially common in storm drain systems. For example, a small storm drain system designed for a five-year frequency discharge may outfall into a major channel associated with a much larger watershed. The two independent events affecting the design are the storm occurring on the small storm drain system and the storm contributing to discharge in the larger watershed.

The simultaneous occurrence of two independent events is defined as the product of the probability of the occurrence of each of the individual events. In other words, if the events are independent, the probability of five-year events occurring on the storm drain and the larger watershed simultaneously is (0.2)2 or 0.04 or 4 percent. This is equivalent to a 25-year frequency.

In ordinary hydrologic circumstances, particularly with adjacent watersheds, flood events are not entirely independent. The “Frequencies for Coincidental Occurrence” table presents suggested frequency combinations for coincidental occurrence. Each design contains two combinations of frequencies; for instance, a five-year design with watersheds of 100 acres (or 1 km2, that is, 1,000,000 m2) and one acre (one hectare , that is, 10,000 m2) that is, 100:1--can employ either of the following scenarios:

  • a two-year design on the main stream and a five-year design on the tributary
  • a five-year design on the main stream and a two-year design on the tributary.

The largest structure required to satisfy both frequency combinations is the five-year design.

Anchor: #i1010484Frequencies for Coincidental Occurrence

Area ratio

2-year design

5-year design

 

main stream

tributary

main stream

tributary

10,000:1

1

2

1

5

 

2

1

5

1

1,000:1

1

2

2

5

 

2

1

5

2

100:1

2

2

2

5

 

2

2

5

5

10:1

2

2

5

5

 

2

2

5

5

1:1

2

2

5

5

 

2

2

5

5

 

10-year design

25-year design

 

main stream

tributary

main stream

tributary

10,000:1

1

10

2

25

 

10

1

25

2

1,000:1

2

10

5

25

 

10

2

25

5

100:1

5

10

10

25

 

10

5

25

10

10:1

10

10

10

25

 

10

10

25

10

1:1

10

10

25

25

 

10

10

25

25

 

50-year design

100-year design

 

main stream

tributary

main stream

tributary

10,000:1

2

50

2

100

 

50

2

100

2

1,000:1

5

50

10

100

 

50

5

100

10

100:1

10

50

25

100

 

50

10

100

25

10:1

25

50

50

100

 

50

25

100

50

1:1

50

50

100

100

 

50

50

100

100


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Rainfall versus Flood Frequency

Drainage structures are designed based on some flood frequency. However, certain hydrologic procedures use rainfall and rainfall frequency as the basic input, with the basic assumption that the flood frequency and the rainfall frequency are the same. Depending on antecedent soil moisture conditions and other hydrologic parameters, this may not be true. For projects on small basins (under 10 sq. mi.) it is usually not practicable to distinguish between rainfall frequency and runoff frequency due to lack of available data.

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